Nature Genetics has a commentary piece and three research papers looking at genetic variants associated with variation in height. First of all, from the commentary piece, we learn that height has a heritability of 0.8, so 80% of variation in height is due to variation in genetics.
The three studies look at hundreds of thousands of SNPs among a total of 63,000 people. Surprisingly they find little overlap in terms of variants that are associated with height in all three studies (variants in only three genes across all three studies, and 7 genes in 2 out of three studies), perhaps due to statistical issues having to do with testing so many variants at once. They find a total of 54 variants that are associated with variation in height, all of them with small effects.
They find no differences between males and females, and no evidence of interaction between alleles.
Throughout this article, the author breaks down the costs and benefits of the various approaches of getting at genotype-phenotype relationships, and discusses some of the other major hurdles in the process.